Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}-9x-y &= -2 \\ 9x-9y &= -8\end{align*}$
Solution: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-10y = -10$ Divide both sides by $-10$ and reduce as necessary. $y = 1$ Substitute $1$ for $y$ in the top equation. $-9x- 1 = -2$ $-9x-1 = -2$ $-9x = -1$ $x = \dfrac{1}{9}$ The solution is $\enspace x = \dfrac{1}{9}, \enspace y = 1$.